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Properties

Label 56550.y
Number of curves $2$
Conductor $56550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 56550.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.y1 56550bb1 \([1, 0, 1, -351, 5248]\) \(-7620530425/14840982\) \(-9275613750\) \([3]\) \(45360\) \(0.60215\) \(\Gamma_0(N)\)-optimal
56550.y2 56550bb2 \([1, 0, 1, 3024, -112202]\) \(4895482323575/11573848728\) \(-7233655455000\) \([]\) \(136080\) \(1.1515\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56550.y have rank \(0\).

Complex multiplication

The elliptic curves in class 56550.y do not have complex multiplication.

Modular form 56550.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 2 q^{7} - q^{8} + q^{9} - 3 q^{11} + q^{12} + q^{13} - 2 q^{14} + q^{16} + 6 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.